Information on Result #657762
Linear OA(25610, 257, F256, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using algebraic-geometric code AG(F,123P) with degPÂ =Â 2 based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
- Extended Reed–Solomon Code [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1620, 514, F16, 10) (dual of [514, 494, 11]-code) | [i] | Trace Code | |
| 2 | Linear OA(1619, 257, F16, 10) (dual of [257, 238, 11]-code) | [i] | Base Reduction for Projective Spaces | |
| 3 | OA(3216, 257, S32, 10) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6414, 257, S64, 10) | [i] | ||
| 5 | OA(12812, 257, S128, 10) | [i] | ||
| 6 | Linear OA(25631, 514, F256, 21) (dual of [514, 483, 22]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25632, 517, F256, 21) (dual of [517, 485, 22]-code) | [i] | ||
| 8 | Linear OA(25651, 65794, F256, 21) (dual of [65794, 65743, 22]-code) | [i] | ||
| 9 | Linear OA(25630, 514, F256, 20) (dual of [514, 484, 21]-code) | [i] | ||
| 10 | Linear OA(25631, 517, F256, 20) (dual of [517, 486, 21]-code) | [i] | ||
| 11 | Linear OA(25649, 65793, F256, 20) (dual of [65793, 65744, 21]-code) | [i] | ||
| 12 | Linear OA(25615, 514, F256, 10) (dual of [514, 499, 11]-code) | [i] | ||
| 13 | Linear OA(25651, 65795, F256, 21) (dual of [65795, 65744, 22]-code) | [i] | ||
| 14 | Linear OA(25652, 65799, F256, 21) (dual of [65799, 65747, 22]-code) | [i] | ||
| 15 | Linear OA(25654, 65805, F256, 21) (dual of [65805, 65751, 22]-code) | [i] | ||
| 16 | Linear OA(25649, 65795, F256, 20) (dual of [65795, 65746, 21]-code) | [i] | ||
| 17 | Linear OA(25632, 546, F256, 21) (dual of [546, 514, 22]-code) | [i] | ||
| 18 | Linear OA(25631, 546, F256, 20) (dual of [546, 515, 21]-code) | [i] | ||
| 19 | Linear OA(25627, 65792, F256, 10) (dual of [65792, 65765, 11]-code) | [i] | Generalized (u, u+v)-Construction | |
| 20 | Linear OA(25613, 260, F256, 12) (dual of [260, 247, 13]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 21 | Linear OA(25611, 260, F256, 10) (dual of [260, 249, 11]-code) | [i] | ✔ | |
| 22 | Linear OA(25617, 264, F256, 14) (dual of [264, 247, 15]-code) | [i] | ✔ | |
| 23 | Linear OA(25613, 264, F256, 10) (dual of [264, 251, 11]-code) | [i] | ✔ | |
| 24 | Linear OA(25621, 268, F256, 16) (dual of [268, 247, 17]-code) | [i] | ✔ | |
| 25 | Linear OA(25615, 268, F256, 10) (dual of [268, 253, 11]-code) | [i] | ✔ | |
| 26 | Linear OA(25625, 272, F256, 18) (dual of [272, 247, 19]-code) | [i] | ✔ | |
| 27 | Linear OA(25629, 276, F256, 20) (dual of [276, 247, 21]-code) | [i] | ✔ | |
| 28 | Linear OA(25633, 280, F256, 22) (dual of [280, 247, 23]-code) | [i] | ✔ | |
| 29 | Linear OA(25637, 284, F256, 24) (dual of [284, 247, 25]-code) | [i] | ✔ | |
| 30 | Linear OA(25641, 288, F256, 26) (dual of [288, 247, 27]-code) | [i] | ✔ | |
| 31 | Linear OA(25645, 292, F256, 28) (dual of [292, 247, 29]-code) | [i] | ✔ | |
| 32 | Linear OA(25649, 296, F256, 30) (dual of [296, 247, 31]-code) | [i] | ✔ | |
| 33 | Linear OA(25615, 262, F256, 13) (dual of [262, 247, 14]-code) | [i] | ✔ | |
| 34 | Linear OA(25612, 262, F256, 10) (dual of [262, 250, 11]-code) | [i] | ✔ | |
| 35 | Linear OA(25627, 274, F256, 19) (dual of [274, 247, 20]-code) | [i] | ✔ | |
| 36 | Linear OA(25639, 286, F256, 25) (dual of [286, 247, 26]-code) | [i] | ✔ | |
| 37 | Linear OA(25619, 266, F256, 15) (dual of [266, 247, 16]-code) | [i] | ✔ | |
| 38 | Linear OA(25614, 266, F256, 10) (dual of [266, 252, 11]-code) | [i] | ✔ | |
| 39 | Linear OA(25658, 66051, F256, 21) (dual of [66051, 65993, 22]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 40 | Linear OA(25655, 66050, F256, 20) (dual of [66050, 65995, 21]-code) | [i] | ||